DLMF:14.15.E12 (Q4858): Difference between revisions

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Revision as of 01:49, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:49, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Q11091
		Property / Symbols used: Q11091 / rank
			Normal rank
		Property / Symbols used: Q11091 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar{x}\right)}}$ \envBesselY{\NVar{\nu}}@{\NVar{x}}
		Property / Symbols used: Q11091 / qualifier
			xml-id: C2.S8.SS4.p5.m4adec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2aadec
		Property / Symbols used
			Q11591
		Property / Symbols used: Q11591 / rank
			Normal rank
		Property / Symbols used: Q11591 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mu}}$ \mu
		Property / Symbols used: Q11591 / qualifier
			xml-id: C14.S1.XMD7.m1hdec
		Property / Symbols used
			Q11590
		Property / Symbols used: Q11590 / rank
			Normal rank
		Property / Symbols used: Q11590 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11590 / qualifier
			xml-id: C14.S1.XMD8.m1hdec
		Property / Symbols used
			Q11615
		Property / Symbols used: Q11615 / rank
			Normal rank
		Property / Symbols used: Q11615 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\theta}}$ \theta
		Property / Symbols used: Q11615 / qualifier
			xml-id: C14.S15.XMD7.m1adec

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Latest revision as of 01:49, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.15.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathsf{Q}^{-\mu}_{\nu}\left(\cos\theta\right)=-\frac{\pi}{2\nu^{\mu}}\left(\frac{\theta}{\sin\theta}\right)^{1/2}\left(Y_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)\theta\right)+O\left(\frac{1}{\nu}\right)\mathrm{env}\mskip-2.0mu Y_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)\theta\right)\right),}}$

0 references

DLMF id

DLMF:14.15.E12

0 references

Symbols used

Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E3.m2adec

0 references

order not exceeding

Defining formula

${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

xml-id

C2.S1.E3.m2agdec

0 references

Ferrers function of the second kind

Defining formula

${\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C14.S3.E2.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2addec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2aadec

0 references

Q11091

Defining formula

${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C2.S8.SS4.p5.m4adec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2aadec

0 references

Q11591

Defining formula

${\displaystyle{\displaystyle\mu}}$

xml-id

C14.S1.XMD7.m1hdec

0 references

Q11590

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C14.S1.XMD8.m1hdec

0 references

Q11615

Defining formula

${\displaystyle{\displaystyle\theta}}$

xml-id

C14.S15.XMD7.m1adec

0 references

 

Sitelinks

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